相关论文: On Generalized Statistics and Interactions
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
Motivated by fractional quantum Hall effects, we introduce a universal space of statistics interpolating Bose-Einstein statistics and Fermi-Dirac statistics. We connect the interpolating statistics to umbral calculus and use it as a bridge…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
The behavior of ecological systems mainly relies on the interactions between the species it involves. We consider the problem of inferring the species interaction network from abundance data. To be relevant, any network inference…
We present a formulation of the deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between the Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of…
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
Generalized planning is concerned with the characterization and computation of plans that solve many instances at once. In the standard formulation, a generalized plan is a mapping from feature or observation histories into actions,…
We provide a general mathematical framework based on the theory of graphical models to study admixture graphs. Admixture graphs are used to describe the ancestral relationships between past and present populations, allowing for population…
The statistical methods used in deriving physics results in the BaBar collaboration are reviewed, with especial emphasis on areas where practice is not uniform in particle physics.
We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical language we correspondingly generalize braidings and the…
Some points concerning the relation of strings to interfaces in statistical systems are discussed.
The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
Bipartite graphs have received some attention in the study of social networks and of biological mutualistic systems. A generalization of a previous model is presented, that evolves the topology of the graph in order to optimally account for…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…